Fine structure of distributions and central limit theorem in diffusive billiards

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz gas where the central limit theorem has been rigorously proved. We study one-dimensional position and displacement densities describing the time evolution of statistical ensembles in a channel geometry, using a more refined method than histograms. We find a pronounced oscillatory fine structure, and show that this has its origin in the geometry of the billiard domain. This fine structure prevents the rescaled densities from converging pointwise to gaussian densities; however, demodulating them by the fine structure gives new densities which seem to converge uniformly. We give an analytical estimate of the rate of convergence of the original distributions to the limiting normal distribution, based on the analysis of the fine structure, which agrees well with simulation results. We show that using a Maxwellian (gaussian) distribution of velocities in place of unit speed velocities does not affect the growth of the mean square displacement, but changes the limiting shape of the distributions to a non-gaussian one. Using the same methods, we give numerical evidence that a non-chaotic polygonal channel model also obeys the central limit theorem, but with a slower convergence rate.Comment: 16 pages, 19 figures. Accepted for publication in Physical Review E. Some higher quality figures at http://www.maths.warwick.ac.uk/~dsander

Plasma etching a ceramic composite

Plasma etching is found to be a superior metallographic technique for evaluating the microstructure of a ceramic matrix composite. The ceramic composite studied is composed of silicon carbide whiskers (SiC(sub W)) in a matrix of silicon nitride (Si3N4), glass, and pores. All four constituents are important in evaluating the microstructure of the composite. Conventionally prepared samples, both as-polished or polished and etched with molten salt, do not allow all four constituents to be observed in one specimen. As-polished specimens allow examination of the glass phase and porosity, while molten salt etching reveals the Si3N4 grain size by removing the glass phase. However, the latter obscures the porosity. Neither technique allows the SiC(sub W) to be distinguished from the Si3N4. Plasma etching with CF4 + 4 percent O2 selectively attacks the Si3N4 grains, leaving SiC(sub W) and glass in relief, while not disturbing the pores. An artifact of the plasma etching reaction is the deposition of a thin layer of carbon on Si3N4, allowing Si3N4 grains to be distinguished from SiC(sub W) by back scattered electron imaging

Review of Recent Searches for Rare and Forbidden Dilepton Decays of Charmed Mesons

I briefly review the results of recent searches for flavor-changing neutral current and lepton-flavor and lepton-number violating decays of D+, Ds, and D0 mesons (and their antiparticles) into modes containing muons and electrons. The primary focus is the results from Fermilab charm hadroproduction experiment E791. E791 examined 24 pi,l,l and K,l,l decay modes of D+ and Ds and l+l- decay modes of D0. Limits presented by E791 for 22 rare and forbidden dilepton decays of D mesons were more stringent than those obtained from previous searches, or else were the first reported.Comment: 8 pages, 1 figure, uses psfig.sty and RevTeX, submitted to Modern Physics Letters A, based on a Fermilab "Joint Theoretical and Experimental" tal

Chaos and stability in a two-parameter family of convex billiard tables

We study, by numerical simulations and semi-rigorous arguments, a two-parameter family of convex, two-dimensional billiard tables, generalizing the one-parameter class of oval billiards of Benettin--Strelcyn [Phys. Rev. A 17, 773 (1978)]. We observe interesting dynamical phenomena when the billiard tables are continuously deformed from the integrable circular billiard to different versions of completely-chaotic stadia. In particular, we conjecture that a new class of ergodic billiard tables is obtained in certain regions of the two-dimensional parameter space, when the billiards are close to skewed stadia. We provide heuristic arguments supporting this conjecture, and give numerical confirmation using the powerful method of Lyapunov-weighted dynamics.Comment: 19 pages, 13 figures. Submitted for publication. Supplementary video available at http://sistemas.fciencias.unam.mx/~dsanders

Deep high-resolution X-ray spectra from cool-core clusters

We examine deep XMM-Newton Reflection Grating Spectrometer (RGS) spectra from the cores of three X-ray bright cool core galaxy clusters, Abell 262, Abell 3581 and HCG 62. Each of the RGS spectra show Fe XVII emission lines indicating the presence of gas around 0.5 keV. There is no evidence for O VII emission which would imply gas at still cooler temperatures. The range in detected gas temperature in these objects is a factor of 3.7, 5.6 and 2 for Abell 262, Abell 3581 and HCG 62, respectively. The coolest detected gas only has a volume filling fraction of 6 and 3 per cent for Abell 262 and Abell 3581, but is likely to be volume filling in HCG 62. Chandra spatially resolved spectroscopy confirms the low volume filling fractions of the cool gas in Abell 262 and Abell 3581, indicating this cool gas exists as cold blobs. Any volume heating mechanism aiming to prevent cooling would overheat the surroundings of the cool gas by a factor of 4. If the gas is radiatively cooling below 0.5 keV, it is cooling at a rate at least an order of magnitude below that at higher temperatures in Abell 262 and Abell 3581 and two-orders of magnitude lower in HCG 62. The gas may be cooling non-radiatively through mixing in these cool blobs, where the energy released by cooling is emitted in the infrared. We find very good agreement between smooth particle inference modelling of the cluster and conventional spectral fitting. Comparing the temperature distribution from this analysis with that expected in a cooling flow, there appears to be a even larger break below 0.5 keV as compared with previous empirical descriptions of the deviations of cooling flow models.Comment: 19 pages, 22 figures, accepted by MNRA

HST/WFC3 Observations of an Off-Nuclear Superbubble in Arp 220

We present a high spatial resolution optical and infrared study of the circumnuclear region in Arp 220, a late-stage galaxy merger. Narrowband imaging using HST/WFC3 has resolved the previously observed peak in H$\alpha$+[NII] emission into a bubble-shaped feature. This feature measures 1.6" in diameter, or 600 pc, and is only 1" northwest of the western nucleus. The bubble is aligned with the western nucleus and the large-scale outflow axis seen in X-rays. We explore several possibilities for the bubble origin, including a jet or outflow from a hidden active galactic nucleus (AGN), outflows from high levels of star formation within the few hundred pc nuclear gas disk, or an ultraluminous X-ray source. An obscured AGN or high levels of star formation within the inner $\sim$100 pc of the nuclei are favored based on the alignment of the bubble and energetics arguments.Comment: Accepted for publication in ApJ. 12 pages, 10 figure

Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries

We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional map when lambda=0 and the classical Hamiltonian case of elastic collisions when lambda=1. For all lambda<1, the dynamics is dissipative, and thus gives rise to attractors, which may be periodic or chaotic. Motivated by recent rigorous results of Markarian, Pujals and Sambarino, we numerically investigate and characterise the bifurcations of the resulting attractors as the contraction parameter is varied. Some billiards exhibit only periodic attractors, some only chaotic attractors, and others have coexistence of the two types.Comment: 30 pages, 17 figures. v2: Minor changes after referee comments. Version with some higher-quality figures available at http://sistemas.fciencias.unam.mx/~dsanders/publications.htm

Keck Absorption-Line Spectroscopy of Galactic Winds in Ultraluminous Infrared Galaxies

In this paper, we present moderately-high resolution (~65 km/s) spectroscopy, acquired with ESI on Keck II, of 11 ultraluminous infrared galaxies at z < 0.3 from the IRAS 1 Jy sample. The targets were chosen as good candidates to host galaxy-scale outflows, and most have infrared luminosities dominated by star formation. We use a chi-squared minimization to fit one- to three-component profiles to the NaI D interstellar absorption doublet in each object. Assuming that gas blueshifted by more than 70 km/s relative to the systemic velocity of the host is outflowing, we detect outflows in 73% of these objects. We adopt a simple model of a mass-conserving free wind to infer mass outflow rates in the range (dM/dt)_tot(H) = 13-133 M_sun/yr for galaxies hosting a wind. These values of (dM/dt)_tot, normalized to the corresponding global star formation rates inferred from infrared luminosities, are in the range eta = (dM/dt)_tot / SFR = 0.1-0.7. This is on average a factor of only 10 less than eta from recent measurements of nearby dwarfs, edge-on spirals, and lower-luminosity infrared galaxies. Within our sample, we conclude that eta has no dependence on the mass of the host (parameterized by host galaxy kinematics and absolute R- and K'-band magnitudes). We also attempt to estimate the average escape fraction = Sum(dM/dt_esc^i) / Sum(dM/dt_tot^i) and ``ejection efficiency'' = Sum(dM/dt_esc^i) / Sum(SFR^i) for our sample, which we find to be \~0.4-0.5 and ~0.1, respectively. The complex absorption-line properties of Mrk 231, an ultraluminous infrared galaxy which is optically classified as a Seyfert 1, are discussed separately in an appendix.Comment: 34 pages, 12 .ps figures, 10 tables; accepted for publication in ApJ, 10 May 2002, v570 n

The Canada-UK Deep Submillimetre Survey: First Submillimetre Images, the Source Counts, and Resolution of the Background

We present the first results of a deep unbiased submillimetre survey carried out at 450 and 850 microns. We detected 12 sources at 850 microns, giving a surface density of sources with 850-micron flux densities > 2.8mJy of of 0.49+-0.16 per square arcmin. The sources constitute 20-30% of the background radiation at 850 microns and thus a significant fraction of the entire background radiation produced by stars. This implies, through the connection between metallicity and background radiation, that a significant fraction of all the stars that have ever been formed were formed in objects like those detected here. The combination of their large contribution to the background radiation and their extreme bolometric luminosities make these objects excellent candidates for being proto-ellipticals. Optical astronomers have recently shown that the UV-luminosity density of the universe increases by a factor of about 10 between z=0 and z=1 and then decreases again at higher redshifts. Using the results of a parallel submillimetre survey of the local universe, we show that both the submillimetre source density and background can be explained if the submillimetre luminosity density evolves in a similar way to the UV-luminosity density. Thus, if these sources are ellipticals in the process of formation, they may be forming at relatively modest redshifts.Comment: 8 pages (LATEX), 6 postscript figures, submitted to ApJ Letter